The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals

TL;DR

This paper develops new analytic techniques for Wilson line integrals and computes the four-loop cusp anomalous dimension in N=4 super Yang-Mills theory, confirming known results and extending understanding to strong coupling regimes.

Contribution

It introduces a novel method for evaluating Wilson line integrals and provides the first four-loop non-planar correction in a specific scaling limit for N=4 SYM.

Findings

Computed the four-loop non-planar correction.

Derived the full planar four-loop cusp anomalous dimension.

Confirmed the four-loop light-like cusp anomalous dimension.

Abstract

Correlation functions of Wilson lines are relevant for describing the infrared structure of scattering amplitudes. We develop a new method for evaluating a wide class of such Wilson line integrals, and apply it to the calculation of the velocity-dependent cusp anomalous dimension in maximally supersymmetric Yang-Mills theory. We compute the four-loop non-planar correction in a recently introduced scaling limit. Moreover, we derive the full planar four-loop result by means of an ansatz which is based on the structure of known analytic results. We determine the coefficients in this ansatz by making use of a relationship to massive scattering amplitudes. As a corollary, our analytical result confirms the four-loop value of the light-like cusp anomalous dimension. Finally, we use the available perturbative data, as well as insight from AdS/CFT, in order to extrapolate the leading order values at strong coupling. The latter agree within two per cent with the corresponding string theory result, over a wide range of parameters.